#include <iostream>
#include <vector>
#include <string>
#include <queue>
#include <unordered_map>
// 成为回文串的最小插入数：https://leetcode.cn/problems/minimum-insertion-steps-to-make-a-string-palindrome/
using namespace std;
class Solution {
public:
    int minInsertions(string s) {
        int n=s.size();
        vector<vector<int>> dp(n,vector<int>(n));
        for(int i=n-1;i>=0;i--)
        {
            for(int j=i+1;j<n;j++)
            {
                if(s[i]==s[j])
                    dp[i][j]=(i+1<j)?dp[i+1][j-1]:dp[i][j];
                else
                    dp[i][j]=1+min(dp[i+1][j],dp[i][j-1]);
            }
        }
        return dp[0][n-1];
    }
};